The possibility of cloaking an object from detection by electromagnetic waves has recently become a topic of considerable interest. Transformation optics is a method for the conceptual design of complex electromagnetic media, offering opportunities for the control of electromagnetic waves. A wide variety of conventional devices can be designed by the transformation optical approach, including beam shifters, beam bends, beam splitters, focusing and collimating lenses, and structures that concentrate electromagnetic waves. Throughout this disclosure, the use of the term “transformation optics” does not imply any limitation with regards to wavelength; a transformation optics device may be operable in wavelength bands that range from radio wavelengths to visible wavelengths and beyond. Moreover, while some exemplary embodiments are designed by a transformation optical approach, other embodiments do not employ a transformation optical approach or do so only partially. Theoretical limitations of the transformation optical approach do not inhere to any embodiments of the broadband metamaterial apparatus, methods, systems, and computer-readable media described herein.
In the transformation optical approach, a transforming from one coordinate system to another can provide an electromagnetic mapping between the two coordinate systems and a set of parameters for the second system that are a function of those of the first system and the transformation. One can envision the transform as a warping of space so as to control the trajectories of light in a desired manner.
As an example of this approach, a cloak can be designed by performing a coordinate transformation that maps the volume of a first three dimensional region (e.g., a sphere having a finite radius) to the volume of a second three dimensional region enclosing a void (e.g., a shell having the same outer radius and a non-zero inner radius).
Waves do not interact with or scatter from the void because it is simply not part of the transformed space. The form invariance of Maxwell's equations implies that the coordinate transformation can instead be applied to the permittivity and permeability tensors, yielding a prescription (e.g., a description of electromagnetic parameters) for a medium that will accomplish the transformed functionality. The resulting medium can be highly complex, anisotropic and with spatial gradients in the components of the permittivity and/or permeability tensors.
Such complicated gradient-index media can be difficult to create with conventional materials but are often easier to build with artificially structured metamaterials, in which spatial variations of the material parameters can be achieved by modifying the physical parameters (such as geometrical parameters) and/or placements of the constituent elements. Previously, metamaterial structures having spatial gradients have been obtained by designing one unit cell at a time until a library of unique metamaterial elements, whose constitutive parameters span the range required by the transformation optical design, is generated. Even so, the large number of elements required in an arbitrary gradient index medium (such as a cloak medium) can represent a substantial computational burden resulting in long design cycles.